High School

For one month, Siera calculated her hometown's average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees Fahrenheit to degrees Celsius using the function [tex]C(F) = \frac{5}{9}(F - 32)[/tex].

What does [tex]C(F)[/tex] represent?

A. [tex]C(F)[/tex] represents the output of the function [tex]C[/tex] in degrees Celsius when the input [tex]F[/tex] is in degrees Fahrenheit.

B. [tex]C(F)[/tex] represents the output of the function [tex]F[/tex] in degrees Fahrenheit when the input [tex]C[/tex] is in degrees Celsius.

C. [tex]C(F)[/tex] represents the output of the function [tex]C[/tex] in degrees Fahrenheit when the input [tex]F[/tex] is in degrees Celsius.

D. [tex]C(F)[/tex] represents the output of the function [tex]F[/tex] in degrees Celsius when the input [tex]C[/tex] is in degrees Fahrenheit.

Answer :

Sure! Let's go through the problem step by step:

Siera wants to convert her home town's average high temperature from degrees Fahrenheit (°F) to degrees Celsius (°C). To do this, she uses the function:

[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]

Here, [tex]\( C(F) \)[/tex] is the expression used to find the temperature in degrees Celsius when the temperature in degrees Fahrenheit is [tex]\( F \)[/tex].

Let's break down the options given for what [tex]\( C(F) \)[/tex] represents:

1. Option 1: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.

2. Option 2: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Fahrenheit when the input [tex]\( C \)[/tex] is in degrees Celsius.

3. Option 3: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Celsius.

4. Option 4: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit.

Now, let's evaluate what each option means:

- Option 1: This correctly states that [tex]\( C(F) \)[/tex] gives us the temperature in degrees Celsius when we start with degrees Fahrenheit. This matches the formula provided.

- Option 2: This incorrectly reverses the roles of Celsius and Fahrenheit. [tex]\( C(F) \)[/tex] is not used to find Fahrenheit from Celsius; it’s the other way around.

- Option 3: This incorrectly states that [tex]\( C(F) \)[/tex] gives a temperature in degrees Fahrenheit when, in fact, it should be Celsius.

- Option 4: This incorrectly suggests using [tex]\( F \)[/tex] when that's part of the input, not the output.

Given our function and understanding, Option 1 is the correct representation of what [tex]\( C(F) \)[/tex] means—converting a temperature from degrees Fahrenheit to degrees Celsius.